Regional Gravity Field Modeling From Heterogeneous Data Sets By Using Possion Wavelets Radial Basis Functions

Determining the fine structure of the earth's gravity field and its time-variable trend is one of the main targets in modern geodesy and solid geophysics. The high-resolution and high-accuracy gravity field reflects the mass distribution and the variation of the earth, which plays an important role in national economic construction, military and national defense compaign as well as in the revelant scientific fields, e.g., geodesy, geophysics, oceanography and geodynamics. Heterogeneous gravity-related data sets could be obtained from various modern geodetic techniques, however, these data sets have different spatial coverage and resolution, various error characteristics as well as different spectral content. Thus, it is difficult to model the high-resolution and high-accuracy gravity field based on the data derived from single data source. Besides, how to make use of these heterogeneous data sets is still an open issue. Under the framework of remove-compute-restore methodology, we mainly study the methodology for regional gravity field modeling by Poisson wavelets radial basis functions based on heterogeneous data sets. The expected research results will be used for providing efficient approach and theoretical model for regional gravity field modeling from heterogeneous data sets.The main work and achievements in this dissertation are as follows:(1) We mainly study the methodolody for regional gravity field modeling by using Possion wavelets radial basis functions (RBFs). By using the Monte-Carlo variance component estimation, the proper weight of the disjunctive observation group could be determined. While, the corresponding approach is designed for deriving the optimal network of RBFs. Based on ScaLAPACK parallelized package, the regional gravity field computed based on huge data could be fast synthesized.(2) The zero- and first-order Tikhonov regularization model is applied for dealing with the ill-conditioned problem in the regional gravity field modeling by Poisson wavelets radial basis functions. In particular, the effect of the choices of the regularization matrices as well as the approaches for estimating the regularization parameter on the solutions is investigated in details. The results show that the regularized solutions with first-order regularization are better than the ones obtained from zero-order regularization method. Moreover, the optimal regularization parameters derived from L-curve, variance component estimation (VCE) and minimum standard deviation (MSTD) approach are quite consistent with each other. Besides, the VCE method estimates the proper weight of disjunctive observation groups as well as regularization parameter simultaneously, which is more efficient.(3) The high-order global gravity model is introduced as reference gravity field to reduce the corresponding linearization errors. The results show that the incorporation of global gravity field model instead of GRS80-derived normal gravity field as the reference gravity field leads a better approximation of the real gravity field, and the corresponding linearization errors are also reduced. Compared to the geoid computed from the GRS80-derived normal gravity field, the accuracy of the geoid based on DGM1S-derived reference gravity field is improved by 1.5 mm,3.3 mm and 9.0 mm at Germany, UK and Norway respectively, where the topography show more undulation.(4) The theoretical problem in residual terrain model (RTM), i.e., the so-called non-harmonic problem, is investigated. We compare the RTM based on prisms and tesseroids and propose the generalized RTM based on tesseroids. The results show that the residual terrain correction based on prism integral has a poor performance in mountainous regions. In flatten regions, the effect of harmonic correction on height anomaly is in mm level, however, this effect reach cm or even dm level in mountainous areas. Compared to original residual terrain model, the generalized one leads a better approximation of the regional gravity filed at the high-frequency part caused by local topographical variation, the accuracy of the geoid computed with the generalized residual terrain model is improved by 1.7 mm and 2.1 cm in UK and Norway, where tend to be mountainous regions.(5) We analyze the effect of topography on the RBFs'network design and the accuracy of the solutions. The results show that the optimal network parameterization over various regions may be different as the effect of topographical masses, and neglecting the high-frequency topographical signal may cause aliasing problem as well as reduce the accuracy of the solutions. After incorporating RTM reduction, the residual gravity field is significantly smoothed and the optimal network design is simplified. In the meanwhile, the accuracy of the gravimetric geoid model is improved by 4 mm in flat areas. While in mountainous area, more significant improvement is obtained if RTM correction is incorporated, with the magnitude of 5 cm.(6) We investigate the effect on the solution caused by using different satellite altimetry-derived observations, i.e., along-track deflection of vertical (DOV) and difference of geoidal height (DGH). Numerical experiments show that using along-track DGH as satellite altimetry observations derives a better geoid model, the accuracy of which is improved by 0.34 cm,0.27 cm,1.4 cm and 2.3 cm in Netherlands, Belgium, UK and relevant marine regions respectively.(7) A global tide model called GOT4.7 and regional tide model named DCSM are evaluated for their performances in geoid modeling. Numerical experiments show the difference between geoid based on different tide models is negligible, which concentrates in shallow water and specific open sea areas. Moreover, the satellite altimetry and shipboard gravity data are complementary with each other in marine gravity field determination, and combining these two datas could improve the accuracy of the solution.(8) We propose the multi-layers of Poisson wavelets'network for multi-scale approximation of regional gravity field based on wavelets decomposition and potential field spectral analysis. We compare the performances of using single-layer and multi-layers of Poisson wavelets'network in regional gravity field modeling. The results show that compared to the solutions derived from single-layer parameterized function model, the solutions obtained from multi-layers network are better. The geoid derived from multi-layers'network is improved by 0.11 cm,0.33 cm and 0.63 cm in Netherlands, Belgium and Germany respectively.(9) A direct approach is proposed to properly combine the GPS/leveling data and gravimetric geoid, where parts of the GPS/leveling data are added to the functional model for geoid solution, which is used for deriving the geoid model that concides with the local region's characteristics. The results show the accuracy of the geoid computed from this function model reach 0.85 cm and 1.64 cm in Netherlands and Belgium, and the mean value of the residuals on GPS/leveling points is-0.08 cm and 0.15 cm respectively, which indicates the systematics errors between these two data sets could be significantly reduced based on the approach we proposed.